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  2. Characteristic equation (calculus) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_equation...

    The characteristic roots (roots of the characteristic equation) also provide qualitative information about the behavior of the variable whose evolution is described by the dynamic equation. For a differential equation parameterized on time, the variable's evolution is stable if and only if the real part of each root is negative.

  3. Characteristic polynomial - Wikipedia

    en.wikipedia.org/wiki/Characteristic_polynomial

    The characteristic equation, also known as the determinantal equation, [1] [2] [3] is the equation obtained by equating the characteristic polynomial to zero. In spectral graph theory , the characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix .

  4. Unit root - Wikipedia

    en.wikipedia.org/wiki/Unit_root

    In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation.

  5. Eigenvalues and eigenvectors - Wikipedia

    en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

    The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor (possibly negative). Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation rotates, stretches, or shears the vectors upon which it acts. Its eigenvectors are those ...

  6. Reciprocal polynomial - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_polynomial

    An antipalindromic polynomial over a field k with odd characteristic is a multiple of x – 1 (it has 1 as a root) and its quotient by x – 1 is palindromic. An antipalindromic polynomial of even degree is a multiple of x 2 – 1 (it has −1 and 1 as roots) and its quotient by x 2 – 1 is palindromic.

  7. Method of characteristics - Wikipedia

    en.wikipedia.org/wiki/Method_of_characteristics

    In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.

  8. Geometrical properties of polynomial roots - Wikipedia

    en.wikipedia.org/wiki/Geometrical_properties_of...

    The complex conjugate root theorem states that if the coefficients of a polynomial are real, then the non-real roots appear in pairs of the form (a + ib, a – ib).. It follows that the roots of a polynomial with real coefficients are mirror-symmetric with respect to the real axis.

  9. Characteristic equation - Wikipedia

    en.wikipedia.org/wiki/Characteristic_equation

    Characteristic equation may refer to: Characteristic equation (calculus), used to solve linear differential equations; Characteristic equation, the equation obtained by equating to zero the characteristic polynomial of a matrix or of a linear mapping; Method of characteristics, a technique for solving partial differential equations

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